Motion compensated reconstruction technique

ABSTRACT

The long scan time in PET imaging may lead to a significant loss of resolution, due to patient or organ motion. According to the present invention, the distortion or motion may be compensated by performing a forward-projection, and/or back-projection of the intermediate image on the basis of a motion field describing a motion and/or distortion of the object of interest.

The present invention relates to the field of digital imaging. Inparticular, the present invention relates to a motion compensated imagereconstruction from projections as in positron emission tomography(PET), single photon emission computed tomography (SPECT) and computedtomography (CT). More specifically, the present invention relates to amethod of reconstructing an image from emission or transmission data ofan object, to an image processing device for reconstructing an imagefrom emission or transmission data, to a PET, SPECT, or CT system and toa computer program product.

In medical imaging techniques known as emission computer tomography,images of an object are created based on the detection of gamma raysemitted from the object. The gamma rays may be emitted from a traceraccumulated in the object. Such a tracer may, for example, be based on¹⁸F-fluorordeoxyglucose. In positron emission tomography (PET),positron-electro annihilations within the object to be imaged causegamma rays to be emitted in pairs of two gamma photons, which fly in(almost) exactly opposite directions. The path formed by each pair ofgamma photons represents a line, which is sometimes referred to as a“line of response”. The specific distribution of the positron emittingcontrast agent or tracer within the object can be determined bycalculating the positions of these lines of coincidence. The aggregateof such information can be used to reconstruct an image.

Energy carried by the gamma photons is typically sensed by detectorsdisposed in an array around the object under study. The detectorsconvert the energy carried by the gamma photons, to record the positionof the event which gave rise to the rays. Electrical signalsrepresentative of the detected gamma photons may be processed by asystem, which typically includes a programmed digital computer capableof processing the position data to form an image of the structure, organor patient under examination. It is the aim of PET-imaging toreconstruct the distribution of the contrast agent or tracer within thehuman body or object. This distribution is called emission image and isreconstructed from the emission measurement or emission data acquired asdescribed above.

The period of time necessary for such measurements depends upon thehalf-time of the tracer or agent used as well as on the maximum countrate that the system can handle and is occasionally ten minutes to 45minutes. Conventionally, the object needed to be fixed both in positionand direction during the measurement period. Such stationary posture maybe very painful to a human body or an animal. Also, the significantlylong scan time leads to significant losses of resolution due to patientor organ motion, in particular for heart and thorax imaging where heartand breathing motion is present during the data acquisition. Also,artifacts due to a motion or deformation of the object of interestappear in the image obtained by image reconstruction. In knowntechniques, only data which belong to a certain phase of the motion areused for reconstruction. This results in less artifacts and sharperimages, but the signal-to-noise-ratio is significantly reduced becausesome data are no longer used for reconstruction.

It is an object of the present invention to provide for an improvedimage reconstruction.

According to an aspect of the present invention, the above object may besolved by a method according to claim 1 for reconstructing an image frommeasured time integrals of an object. According to this exemplaryembodiment of the present invention, the measured line-integrals arebinned into a plurality of temporal bins, a plurality of motion fieldsis determined for the plurality of temporal bins and first data areselected from a selected bin of the plurality of temporal bins. Then, anintermediate image is forward-projected for forming second data by usinga motion field of the plurality of motion fields that belongs to theselected temporal bin. Then, a difference between the first data and thesecond data is determined and the intermediate image is up-dated on thebasis of the difference.

Advantageously, the above method takes a motion and deformation of theobject of interest into account. Furthermore, it may still allow tomaximize a likelihood function. Overall, according to this exemplaryembodiment of the present invention, even in the presence of motion ordeformation in the object of interest, a proper reconstruction may berealized, yielding a sharp image with high signal-to-noise-ratio.

Claims 2 to 6 provide for further advantageous embodiments of thepresent invention.

Another exemplary embodiment of the present invention as set forth inclaim 7 provides for an image processing device for reconstructing animage from measured line integrals, which, e.g. during thereconstruction of a PET image, takes into account a motion and/ordeformation of the object of interest.

Another exemplary embodiment of the present invention as set forth inclaim 8 provides for a positron emission tomography system, which mayinclude a scanner system, such as the one, for example, depicted in U.S.Pat. No. 5,703,369, which is hereby incorporated by reference, whichallows for sharp PET images, even in the case of a moving, and/ordeforming object of interest.

According to another exemplary embodiment of the present invention asset forth in claim 9, a computer program product comprising a computerprogram is provided, causing a processor to perform an operation whenthe computer program is executed on the processor, corresponding to themethod according to the present invention. The computer program may bewritten in any suitable programming language, for example, in C++. Thecomputer program product may be stored on a computer readable mediumsuch as a CD-ROM. Also, these computer programs may be available from anetwork, such as the WorldWideWeb, from which they may be downloadedinto image processing units or processors, or any suitable computers.

It may be seen as the gist of an exemplary embodiment of the presentinvention that a motion compensated iterative reconstruction techniquefor reconstructing an image from measured line integrals is provided,taking a motion and/or deformation of the object of interest intoaccount. In particular, according to an aspect of the present invention,the forward projection of the iterative reconstruction technique isperformed on the basis of a motion field describing at least one of amotion or deformation of the object with respect to a reference grid ofthe intermediate image.

These and other aspects of the present invention will become apparentfrom and will be elucidated with reference to the embodiments describedhereinafter.

Exemplary embodiments of the present invention will be described in thefollowing, with reference to the following drawings:

FIG. 1 shows a schematic representation of an image processing deviceaccording to an exemplary embodiment of the present invention, adaptedto execute an exemplary embodiment of a method according to the presentinvention.

FIG. 2 shows a flowchart of an exemplary embodiment of an operation ofthe image processing device of FIG. 1 in accordance with the presentinvention.

FIG. 3 shows a simplified schematic representation for furtherexplaining the present invention.

FIG. 4 shows another simplified schematic representation for furtherexplaining the present invention.

FIG. 1 shows an exemplary embodiment of an image processing deviceaccording to the present invention. The image processing device shown inFIG. 1 includes an image processing and control processor 1, with amemory 2, in which the measured line integrals, for example, thedetected sinogram and an intermediate image generated and/or updatedduring the operation may be stored. The image processing and controlprocessor (CPU) 1 may be coupled, via a bus system 3, to an imagingdevice (not shown in FIG. 1), for example, a PET scanner, such as theone described in U.S. Pat. No. 5,703,369, which is hereby incorporatedby reference. An image generated by the image processing and controlprocessor 1 may be displayed to an operator on a monitor 4, connected tothe image processing and control processor 1. The operator may accessthe image processing and control processor 1 via a keyboard 5 or otherinput means, which are not shown in FIG. 1, such as a mouse or atrackball.

Furthermore, via the bus system 3, it is also possible to connect theimage processing and control processor 1 to, for example, a motionmonitor, which monitors a motion of the object of interest. In case, forexample, a lung of a patient is imaged, the motion sensor may be anexhalation sensor. In case the heart is imaged, the motion sensor may bean electrocardiogram (ECG).

FIG. 2 shows a flowchart of a method for operating the image processingdevice depicted in FIG. 1 in accordance with an exemplary embodiment ofthe present invention.

After the start in step S1, the emission data is acquired in step S2.This may, for example, be done using a suitable PET scanner or byreading the emission data from a storage. The emission data consists ofa plurality of line-integrals of the unknown tracer concentrationrelating to the position and/or orientation of the line of response(LOR) on which the event was happening and the integral of the eventsover the measurement time. Typically events with the same or almost thesame LOR are added to from a so-called line integral. Furthermore, lineintegrals, which belong to parallel LORs, are grouped together. Such agroup is called projection. The data structure containing projectionsfrom 0 to 180 degrees is usually referred to as sinogram. Here, in thesubsequent step S3, according to an aspect of the present invention,events of the emission data are binned additionally into temporal bins.However, according to an aspect of the present invention, the presentinvention may also be applied to spatially non-binned single events byusing so-called list-mode reconstruction.

Each temporal bin belongs to a certain motion state. In other words, incase an organ with a more or less periodical motion is imaged, theemission data is rearranged such that projections acquired at a similarphase or motion state are binned into the same temporal bin. Thedecision as to which temporal bin an event belongs may be made on thebasis of information acquired by means of a motion sensor, such as, forexample, an exhalation sensor or an electrocardiogram. According to anaspect of the present invention, it may also be possible to useintrinsic information in the emission data itself, such as the center ofgravity of the events averaged at a few ten or hundred milliseconds asdescribed in further detail in “Four-dimensional affine registrationmodels for respiratory-gated PET”, Klein, G. J.; Reutter, R. W.;Huesman, Nuclear Science, IEEE Transactions on, Volume: 48 Issue: 3,June 2001 Page(s): 756-760, which is hereby incorporated by reference.

A three dimensional image is reconstructed from each temporal bin usingstandard reconstruction techniques. These images may be reconstructed ina low resolution in order to obtain a reasonable signal-to-noise-ratioand to keep the computational cost modest. A motion field describing themotion of the image relative to a chosen reference image (which can befor instance the image with the highest signal-to-noise-ratio) isdetermined for each image in step S4. A motion field describes a motionand/or deformation of the object of interest at a certain point of time.The motion field may be determined in accordance with the methoddescribed in T. Schäffter, V. Rasche, I. C. Carlsen, “Motion CompensatedProjection Reconstruction”, Magnetic Resonance in Medicine 41: 954-963(1999), which is hereby incorporated by reference.

FIG. 3 shows examples of such motion fields. The left side of FIG. 3shows an undisturbed reference motion field and the motion field on theright side of FIG. 3 shows another motion state where the grid of themotion field is deformed. In comparison to the left side of FIG. 3, thegrid points r_(i) in the grid on the right side of FIG. 3 are displacedby a vector Δ_(i) due to the motion.

In other words, the grid points r_(i) of the grid of the motion fieldsdescribe the local motion or deformation of the object of interest.

Then, the method continues to step S5, where a first intermediate imageA₀(x,y) is determined. The first intermediate image A₀(x,y) may, forexample, be a homogenous distribution, a filtered-back projection of theemission data or a simple back-projection of the emission data. Then, inthe next step S6, a counter is initiated with n=0. In the subsequentsteps S7 to S12, the motion compensated iterative image reconstructionis performed.

In step S7, the intermediate image A_(0+n)(x,y), in the case of thefirst iteration, the first intermediate image determined in step S5, isforward-projected by using the motion fields corresponding to theprojection. In other words, the intermediate image A_(0+n)(x,y) isforward-projected by using motion or deformation information gatheredfrom the motion field corresponding to the motion of the object ofinterest at such point in time.

Then, in the subsequent step S8, the forward projected A_(0+n)(x,y) iscompared to a corresponding projection of the emission data to determinea difference between the projected intermediate image A_(0+n)(x,y) andthe projection actually measured. In other words, in step S8, acomparison is made between the motion and/or deformation compensatedintermediate image and the projection actually measured at the time. Ina simple case, the difference may simply be determined on the basis of asubtraction.

Then, the method continues to step S9, where the difference or errordetermined in step S8 is back-projected by using the motion field usedin step S7. This may simply be done by storing the integration weightsof the individual voxels of the intermediate image A_(0+n)(x,y) duringthe forward-projection in step S7. These integration weights define howstrongly the voxel contributed to the line integrals. The same weightscan be applied after proper normalization during the back-projection instep S9. This results in a new (updated) intermediate image A_(1+n)(x,y)in step S9. Then, the method continues to step S10, where it isdetermined whether an end criterion is met or not. The end criterionmay, for example, be that the iteration was performed for allprojections of the emission data or that the differences between theprojection actually measured and the intermediate image A_(0+n)(x,y) arebelow a predetermined threshold. In case it is determined in step S10that the end criterion is not met, the method continues to step S11,where the counter n is incremented: n=n+1. Then, the method continues tostep S7, where the new intermediate image determined in step S9 isforward-projected. Then, steps S7 to S11 are iteratively repeated untilthe end criterion is met. In case it is determined in step S10 that theend criterion is met, the method continues to step S12, where it ends.

In other words, as described above, during iterative reconstruction, theintermediate image A_(0+n)(x,y) is updated based on the information of aselected projection (or a selected line of response LOR). Eachprojection belongs to a certain motion state and the position of thegrid points r_(i) are displaced by a vector Δ_(i) due to the motion.Then, as indicated with reference to step S7, in the forward-projection,the contribution of the activity located at each grid point to thesignal in the selected projection is calculated. According to thepresent invention, in this step, the true position r_(i)+Δ_(i) of thegrid point in the current motion state is used, thus allowing for acompensation of the motion. Furthermore, according to an aspect of thepresent invention, the local deformation of the gird is taken intoaccount. The local topology is critical, since the image value at a gridpoint represents the activity in the neighborhood of the grid point. Thedistribution of the activity over the neighborhood is usually referredto as basis function. Basis functions are, for example, voxels or blobs.According to the present invention as described above, the shape of thebasis function is also subjected to the local deformation derived fromthe motion field. As described with reference to FIG. 2, this is made byusing the respective motion field, corresponding to the projection inthe forward-projection in step S7 and the back-projection in step S9. Ina first approximation, a rotation, a sheering and/or a stretching orcompression may describe such local deformation. After deformation, theblob may be renormalized, in order to ensure that the normal activityrepresented by the image is invariant.

As mentioned above, FIG. 3 shows two motion fields: on the left side, afirst motion field, including a rectangular, not deformed grid belongingto the reference temporal bin; on the right side of FIG. 3 there isdepicted a second deformed grid, where the grid points are displaced byvectors Δ_(i). The motion field on the left side of FIG. 3 is the motionfield of reference image A_(0+n)(x,y). The motion field on the rightside of FIG. 3 describes the motion and/or deformation of the object ofinterest at a time point t_(i) in comparison to the reference grid orreference motion field shown on the left side of FIG. 3. As mentionedabove, as the basis function for describing an activity in theneighborhood of the grid points r_(i), a blob may be used. On the leftside of FIG. 3, an undisturbed blob at a grid point r_(i) at thereference grid is shown. The right side of FIG. 3 shows the displacementand distortion of the same blob after taking the motion and thedistortion of the object of interest into account. As may be taken fromthe right side of FIG. 3, in comparison to the left side of FIG. 3, froma circular form on the left side, the blob has been distorted to anegg-like shape on the right side of FIG. 3. Furthermore, the position ofthe blob has moved to the right side and the breadth of the blob hasincreased.

The left side of FIG. 4 shows a 3D view of a 2D standard blob. The rightside of FIG. 4 shows the view of the blob if the local deformation was acompression by a factor of 1.5 in one direction.

Thus, according to an aspect of the present invention, the referenceimage A_(0+n)(x,y) is forward-projected by using the motion field suchthat it is projected, motion and deformation corrected, onto therespectively measured projection of the emission data. Thus, by alsotaking this motion and deformation information into account byback-projecting the correction factors for the intermediate image, eachbasis function, i.e. voxel or blob of the intermediate image is onlyupdated with the immediately and directly corresponding information fromthe respective projection of the emission data by which a blurring orsmearing effect in the final image can be avoided and a sharp PET imagecan be provided.

According to an aspect of the present invention, all data are used in asingle reconstruction process in order to maximize the common likelihoodfunction of the image. Furthermore, as apparent to the skilled person,the above described technique may be applied to all known iterativereconstruction techniques known in PET, SPECT or CT imaging, such as,for example, RAMLA, ME-ML, OS-ME-ML, or ART.

1. A method of reconstructing an image from measured line-integrals ofan object, the method comprising the steps of: binning of the measuredline-integrals into a plurality of temporal bins; determining aplurality of motion fields for the plurality of temporal bins; selectingfirst data from a selected bin of the plurality of temporal bins;forward-projecting an intermediate image for forming second data byusing a motion field of the plurality of motion fields that belongs tothe selected temporal bin; determining a difference between the firstdata and the second data; up-dating the intermediate image on the basisof the difference.
 2. The method according to claim 1, wherein theintermediate image is up-dated on the basis of a back-projectionperformed by using the motion field that belongs to the selectedtemporal bin.
 3. The method according to claim 1, wherein the pluralityof motion fields contains information with respect to a location shiftand a local deformation of basis functions of the intermediate imagewith regard to the measured line-integrals.
 4. The method according toclaim 1, wherein the steps of claim 1 are iteratively performed until anend criterion has been fulfilled.
 5. The method according to claim 1,wherein the plurality of motion fields describes at least one of amotion and deformation of the object with respect to a reference grid ofthe intermediate image.
 6. The method according to claim 1, wherein theplurality of motion fields is determined from a set of images where eachimage is reconstructed using data from one temporal bin of the pluralityof temporal bins only.
 7. An image processing device for reconstructingan image from measured line-integrals, comprising: a storage for storingthe positron emission data; and an image processor for reconstructingthe image from the measured line-integrals; wherein the image processoris adapted to performs the following operation: binning of the measuredline-integrals into a plurality of temporal bins; determining aplurality of motion fields for the plurality of temporal bins; selectingfirst data from a selected bin of the plurality of temporal bins;forward-projecting an intermediate image for forming second data byusing a motion field of the plurality of motion fields that belongs tothe selected temporal bin; determining a difference between the firstdata and the second data; and up-dating the intermediate image on thebasis of the difference.
 8. A positron emission tomography system,wherein the positron emission tomography system includes a storage forstoring measured line-integrals and an image processor, wherein theimage processor performs the following operation: binning of themeasured line-integrals into a plurality of temporal bins; determining aplurality of motion fields for the plurality of temporal bins; selectingfirst data from a selected bin of the plurality of temporal bins;forward-projecting an intermediate image for forming second data byusing a motion field of the plurality of motion fields that belongs tothe selected temporal bin; determining a difference between the firstdata and the second data; up-dating the intermediate image on the basisof the difference.
 9. A computer program stored on a computer readablemedium comprising computer program means to cause a processor to executethe following steps when the computer program means are executed on theprocessor: binning of the measured line-integrals into a plurality oftemporal bins; determining a plurality of motion fields for theplurality of temporal bins; selecting first data from a selected bin ofthe plurality of temporal bins; forward-projecting an intermediate imagefor forming second data by using a motion field of the plurality ofmotion fields that belongs to the selected temporal bin; determining adifference between the first data and the second data; up-dating theintermediate image on the basis of the difference.